(n^2+n)/2=1225

Solution for (n^2+n)/2=1225 equation:

(n^2+n)/2=1225

We move all terms to the left:

(n^2+n)/2-(1225)=0

We multiply all the terms by the denominator


(n^2+n)-1225*2=0

We add all the numbers together, and all the variables

(n^2+n)-2450=0

We get rid of parentheses

n^2+n-2450=0

a = 1; b = 1; c = -2450;
Δ = b2-4ac
Δ = 12-4·1·(-2450)
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-99}{2*1}=\frac{-100}{2}
=-50
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+99}{2*1}=\frac{98}{2}
=49
$